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The length of the perpendicular from the...

The length of the perpendicular from the origin to the plane passing through the points `veca` and containing the line `vecr = vecb + lambda vecc` is

A

`([vecavecbvecc])/(|vecaxxvecb+vecbxxvecc+veccxxveca|)`

B

`([vecavecbvecc])/(|vecaxxvecb+vecbxxvecc|)`

C

`([vecavecbvecc])/(|vecbxxvecc+veccxxveca|)`

D

`([vecavecbvecc])/(|veccxxveca+vecaxxvecb|)`

Text Solution

Verified by Experts

The correct Answer is:
c
The given plane passes through `veca` and is parallel to the vectors `vecb-vecaandvecc`. So it is normal to
`(vecb-veca)xxvecc`. Henec, its equation is `(vecr-veca).((vecb-veca)xxvecc)=0`
or `vecr.(vecbxxvecc+veccxxveca)=[vecavecbvecc]`
The length of the perpendicular from the origin to this plane is
`[vecavecbvecc]/(|vecbxxvecc+veccxxveca|)`
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